Appendix 3 - Design Calculations for Soak Pits and ......Appendix 3 - Design Calculations for Soak...
Transcript of Appendix 3 - Design Calculations for Soak Pits and ......Appendix 3 - Design Calculations for Soak...
Appendix 3 - Design Calculations for Soak Pits and Infiltration Trenches – Tables and
Equations
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1 Introduction
This Appendix will explain how to design soak pits and infiltration trenches. It contains the following information:
Design tables for soak pits and infiltration trenches
Explanations of the equations used for soak pit and infiltration trench calculations
Step-by-step sample calculations with full solutions
Practice questions with full solutions
2 Calculations Using Design Tables
There are five pieces of information that must be considered to design a soak pit or infiltration trench: `
Key Information Needed for Soak Pit and Infiltration Trench
1.
1. Infiltration area (iA): The surface area required to infiltrate the amount of wastewater entering the pit. IMPORTANT: This is the surface area of just the sides of the pit. This does not include the surface area of the bottom or top of the pit. This is because the bottoms clogs quickly and does not infiltrate very much water.
2. Pit dimensions
Length (L) and width (W) for a rectangular or square pit.
Diameter (d) (the distance from one side of the circle to the opposite through the middle) for a circular pit.
3. Soil infiltration rate (iR): The rate at which water moves from the pit into the
soil. This depends on the characteristics of the soil. 4. Wastewater loading (Q): The amount of wastewater entering the pit
throughout a day.
5. Pit depth (D): How deep the pit is.
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2.1 Pit Shape
Choose the type of pit and shape of the pit before starting any calculations or using the tables. When choosing, remember the following:
Circular pits are less likely to collapse because the pressure from the surrounding soil is evenly spread.
Rectangular pits tend to collapse more often because pressure is placed on the four walls. This leaves the corners to absorb the stress.
Pressure from surrounding
ground
Pressure from surrounding
ground
(Lifewater, 2009)
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Pit Dimensions
Depth (D)
Diameter (d)
Circular Pit
Length (L)
Depth (D)
Infiltration Trench
Length (L)
Depth (D)
Width (W)
Rectangular Pit
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2.2 Soil Type
You must know the type of soil to use the tables and make sure you get the right design. Table 2.2.1 shows the types of soil and their physical descriptions.
Table 2.2.1 - Types of Soil and their Physical Description
Soil Type Physical Description
Gravel, coarse and medium sand Moist soil will not stick together
Fine and loamy sand Moist soil sticks together but will not form a ball
Sandy loam and loam Moist soil forms a ball but still feels gritty when rubbed between the fingers
Loam, porous silt loam Moist soil forms a ball which easily deforms and feels smooth between the fingers
Silty clay loam and clay loam Moist soil forms a strong ball which smears when rubbed but does not go shiny
Clay* Moist soil moulds like plasticine and feels sticky when wetter
(Harvey, Baghri, & Reed, 2002)
* Clay is not suitable for soak pits or trenches since it is difficult for the water to move into.
2.3 Soak Pit and Infiltration Trench Design Tables
This section provides tables that can be used to design a soak pit or infiltration trench. The tables were calculated assuming that the pits will be lined and not filled with rocks. You may want to slightly increase the dimensions of your soak pit if you will be filling it with rocks instead of lining it. The tables found below can be used to design soak pits or infiltration trenches for inputs of 80, 120 and 160 litres of wastewater daily. These tables do not cover all possible options. If none of the options in these tables are appropriate for your needs, then you will have to design your soak pit or infiltration trench by hand. Section 3 in this appendix explains how to do this.
Practical Considerations 1. A pit deeper than 1.2 metres should be supported by pit lining or shoring (a
temporary support structure) while digging. This will help to prevent it from collapsing on the person digging.
2. The bottom of the pit must be 1.5 metres above the water table.
3. Infiltration trenches are long, narrow (about the width of a shovel) and shallow.
They usually require more space and materials but can infiltrate a larger amount of water than a soak pit.
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Table 2.3.1 - Soak Pit Design for 1 metre Diameter or 1 x 1 metre Square
Table 2.3.2- Soak Pit Design for 1.2 metre Diameter or 1.2 x 1.2 metre Square
Soil Type
Pit Depth (metres)
80 litres Daily 120 litres Daily 160 litres Daily
Circle Square Circle Square Circle Square
Gravel, coarse and medium sand
0.5 0.4 0.8 0.6 1.0 0.8
Fine and loamy sand
0.8 0.6 1.2 0.9 1.5 1.2
Sandy loam and loam
1.1 0.8 1.6 1.3 2.1 1.7
Loam, porous silt loam
1.4 1.1 2.1 1.7 2.8 2.2
Silty clay loam and clay loam
3.2 2.5 4.8* 3.8* 6.4* 5.0*
Soil Type
Pit Depth (metres)
80 litres Daily 120 litres Daily 160 litres Daily
Circle Square Circle Square Circle Square
Gravel, coarse and medium sand
0.4 0.3
0.6 0.5 0.8 0.7
Fine and loamy sand
0.6 0.5 1.0 0.8 1.3 1.0
Sandy loam and loam
0.9 0.7 1.3 1.0 1.8 1.4
Loam, porous silt loam
1.2 0.9 1.8 1.4 2.4 1.9
Silty clay loam and clay loam
2.7 2.1 4.0 3.1 5.3 4.2
Important information for Soak Pit Tables
The tables are calculated assuming a concrete slab will be placed as a cover. If your soak pit will be buried underground, you will need space for cover, drainage and backfill. For buried pits add at least 0.2 metres onto the value found in the table.
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Table 2.3.3 - Infiltration Trench Design for 0.5 metre deep trench (not including depth of cover)
Table 2.3.4 - Infiltration Trench Design for a 1.0 metre deep trench (not including depth of cover)
Soil Type
Trench Length (metres)
80 litres Daily 120 litres Daily 160 litres
Daily
Gravel, coarse and medium sand
1.6
2.4 3.2
Fine and loamy sand
2.4 3.6 4.8
Sandy loam and loam
3.3 5.0 6.7
Loam, porous silt loam
4.4 6.7 8.9
Silty clay loam and clay loam
10.0 15.0 20.0
Soil Type
Trench Length (metres)
80 litres Daily 120 litres Daily 160 litres
Daily
Gravel, coarse and medium sand
0.8 1.2 1.6
Fine and loamy sand
1.2 1.8 2.4
Sandy loam and loam
1.7 2.5 3.3
Loam, porous silt loam
2.2 3.3 4.4
Silty clay loam and clay loam
5.0 7.5 10.0
Important information for Infiltration Trench Tables
These tables were calculated with a 0.5 metre depth and a 1.0 metre depth. When you actually go to build the trench dig at least 0.2 metres deeper so that there is space for soil cover. For example, if you want a depth of pit 0.5 metres you must dig 0.7 metres deep and for a 1.0 metre depth you must dig 1.2 metres deep.
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2.4 Soak Pit and Infiltration Trench Design Table Practice Questions
Use the tables in Section 2.3 and Table 2.2.1 to answer the following questions. Solutions are found at the end of this section.
Question 1
A family wants to build a rectangular soak pit
They need to dispose of 80 litres of wastewater each day
They want to make it 1 metre by 1 metre
They are digging in sandy loam
How deep should their pit be?
Question 2
A family wants to build a circular soak pit
They need to dispose of 80 litres of wastewater each day
They want to make it with a 1 metre diameter
They are digging in sandy loam
How deep should their pit be?
Question 3
A family wants to build a circular soak pit
They need to dispose of 120 litres of wastewater each day
They want to make it with a 1.2 metre diameter
They are digging in fine and loamy sand
How deep should their pit be?
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Question 4
A family wants to build a rectangular soak pit
They need to dispose of 80 litres of wastewater each day
They want to make it 1.2 x 1.2 metres
They are digging in silty clay loam
How deep should their pit be?
Question 5
A family wants to build a rectangular soak pit
They need to dispose of 120 litres of wastewater each day
They want to make it 1.2 x 1.2 metres
They are digging in a soil that sticks together but won‟t form a ball
How deep should their pit be?
Question 6
A family wants to build an infiltration trench.
They need to dispose of 80 litres of wastewater each day
The depth of the trench walls is 0.5 metres
They are digging in sandy loam
How long should their trench be? How deep do they have to dig to account for 0.2 metres of cover?
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Question 7
A family wants to build an infiltration trench
They need to dispose of 160 litres of wastewater each day
The depth of the trench walls is 1.0 metres
They are digging in a soil that forms a strong ball which smears when rubbed but doesn‟t go shiny
How long should their trench be? How deep do they have to dig to account for 0.2 metres of cover?
Question 8 (Challenge Question)
A family wants to build a rectangular soak pit
They need to dispose of 100 litres of wastewater each day
They want to make it 1.2 x 1.2 metres
They are digging in a soil that sticks together but won‟t form a ball
How deep should their pit be?
Question 9 (Challenge Question)
A family wants to build a circular soak pit
They need to dispose of 140 litres of wastewater each day
They want to make it with a 1.2 metre diameter
They are digging in a sandy loam
How deep should their pit be?
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Question 10 (Challenge Question)
A family wants to build an infiltration trench
They need to dispose of 100 litres of wastewater each day
The depth of the trench walls is 0.5 metres
They are digging in a soil that forms a ball which easily deforms and feels smooth between the fingers
How long should their trench be?
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Solutions to Practice Questions 1) Using Table 2.3.1, D = 0.8 metres
2) Using Table 2.3.1, D = 1.1 metres
3) Using Table 2.3.2, D = 1.0 metres
4) Using Table 2.3.2, 2.1 metres
5) Using Table 2.2.1, Soil = Fine and Loamy Sand, Using Table 2.3.2, D = 0.8 metres
6) Using Table 2.3.3, D = 3.3 metres, Dig = 3.5 metres
7) Using Table 2.2.1, Soil = Silty Clay Loam and Clay Loam, Using Table 2.3.4, D = 4.4 metres, Dig = 4.6 metre
8) Using Table 2.2.1, Soil = Fine and Loamy Sand Step 1: 80 litres, Using Table 2.3.2, D = 0.5 metres Step 2: 120 litres, Using Table 2.3.2, D = 0.8 metres Step 3: 100 litres, Halfway between answers of step 1 and step 2, D = 0.7 metres
9) Step 1: 120 litres, Using Table 3.3.2, D = 1.3 metres Step 2: 160 litres, Using Table 3.3.2, D = 1.8 metres Step 3: 140 litres, Halfway between answers of step 1 and step 2, D = 1.6 metres
10) Using Table 2.2.1, Soil = Loam, Porous Silt Loam Step 1: 80 litres, Using Table 2.3.3, D = 4.4 metres Step 2: 120 litres, Using Table 2.3.3, D = 6.7 metres Step 3: 100 litres, Halfway between answers of step 1 and step 2, D = 5.6 metres
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3 Calculations by Hand
This section will explain the equations that are used in soak pit and infiltration pit design calculations. It will then lead you through sample and practice questions.
3.1 Calculating Infiltration Area for Pits and Trenches Based on Dimensions
We will start with the pit shapes and the equations that are needed to figure out infiltration area.
3.1.1 Rectangular Pit
Infiltration area for a rectangular pit can be calculated from the three pit dimensions
Depth
Length
Width
A rectangular pit shape is made of 3 sets of rectangles that have different dimensions.
1. Top and bottom are the same
2. Front and back are the same
3. Side and side are the same
Length (L)
Depth (D)
Width (W)
Rectangular Pit
Length (L)
Depth (D)
Infiltration Trench
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Length (L)
Width (W)
Top and Bottom
This is the shape that you see when you look at the pit from above. The length and width of the pit are most likely determined by the size of slab you have or can build.
Front and Back
You create the depth as you dig your pit. The front and back rectangle shares the length dimension of the top and bottom rectangle. The dimensions of this rectangle are length (L) and depth (D).
Side and Side
The side and side rectangle has the same depth (D) as the front and back rectangles. It also has the same width (W) as the top and bottom rectangles.
Note: All dimensions used in this appendix are measured in metres.
Length (L)
Depth (D)
Width (W)
Depth (D)
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Infiltration Area
Area of Front and Back Rectangles
DLA
DepthLengthArea
Length and depth are measured in metres (m)
Surface area is measured in square metres (m2)
Area of Side and Side Rectangles
DWA
DepthWidthArea
The side and side rectangle has the same depth (D) as the front and back rectangles.
Important information
In soak pit calculations, infiltration area refers to the total area of all the sides of the rectangle (this does not include the top and bottom because the bottom clogs so quickly).
In infiltration trench calculations, infiltration area refers to the total area of only the two long sides (it does not include the top and bottom because the bottom clogs quickly or the two ends (side and side) because that area is so small). In an infiltration trench the length will always be larger than the depth.
Length (L)
Depth (D)
Width (W)
Depth (D)
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Soak Pit Infiltration Area The infiltration area of the pit is the total area of the front, back and two sides.
)WL(D2iA
)DL(2)DL(2iA
)DW()DW()DL()DL(iA
area Side area Side area Back area Front area onInfiltrati
Infiltration Trench Infiltration Area The infiltration area of the trench is the total area of the front and back.
DL2 iA
D)(L D)(L iA
area Back area Front area onInfiltrati
This equation can be rearranged to find length.
D2
iAL
Practical Consideration
Usually, infiltration trenches are not deeper than about 1 metre. This is because it is easier to dig a long shallow trench rather than a deep trench. A soak pit may better meet your needs if you are going much deeper than 1 meter.
Infiltration trenches require a soil cover. Cover is normally at least 0.2 metres. Remember to add this to your total depth after doing your calculations. This is how deep you will actually dig.
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3.1.2 Circular Pit
Infiltration area for a circular pit can be calculated from the two pit dimensions: depth and diameter (the distance across the circle through the middle).
A circular pit shape is called a cylinder. It is made up of two identical circles that are the top and the bottom, and a rectangle that wraps around them. If you were to unroll a cylinder and lay it flat on the ground it would look like this:
Important information
In soak pit calculations, infiltration area refers to the total side area of a circular pit (this does not include the top and bottom). This is because the bottom will clog very quickly and not infiltrate much water.
Diameter (d)
Depth (D)
Length (L)
Depth (D)
Diameter (d)
Circular Pit
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Diameter (d)
The rectangular part of the unrolled cylinder is the sides of the pit, therefore the area of this rectangle is the infiltration area.
DLiA
DepthLength AreaonInfiltrati
Length and depth are measured in metres (m)
Surface area is measured in square metres (m2)
When designing a circular pit we do not know the length of the rectangle. What we do know is that the length of the rectangle is equal to the distance around one of the circles, also known as circumference of a circle. We can figure out the circumference and therefore the length based on the diameter of the pit.
14.3dL
14.3DiameterLength
Diameter is measured in metres (m)
Length is measured in metres (m)
3.14 is a rounded value for the ratio pi (π)
Therefore, the equation for the infiltration area of a circular pit is:
D14.3diA
DLiA
DepthLength AreaonInfiltrati
Depth (D)
Length (L)
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3.2 Calculating Infiltration Area Based on Usage
The following equation tells us how much infiltration area is needed based on how much water will be entering the pit.
iR
QiA
rate oninfiltrati Soil
loading Wastewater area onInfiltrati
The following table provides values that should be used for soil infiltration rates based on the type of soil where the pit will be dug.
Table 3.1.3.1 - Typical Infiltration Rates According to Soil Type
Soil Type Physical Description Infiltration Rate of Wastewater(L/m2/day)
Gravel, coarse and medium sand
Moist soil will not stick together
50
Fine and loamy sand Moist soil sticks together but will not form a ball
33
Sandy loam and loam Moist soil forms a ball but still feels gritty when rubbed between the fingers
24
Loam, porous silt loam Moist soil forms a ball which easily deforms and feels smooth between the fingers
18
Silty clay loam and clay loam Moist soil forms a strong ball which smears when rubbed but does not go shiny
8
Clay* Moist soil moulds like plasticine and feels sticky when wetter
Unsuitable for soak pits or infiltration trenches.
Wastewater loading is how much water is entering the pit daily.
Soil infiltration rate is how fast the water entering the pit can move through the soil.
This rate is taken from table 3.1.3.1 and is based on the type of soil.
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(WEDC, 2002)
If the soil type is cannot be determined based on table 3.1.3.1 an infiltration rate test can be done.
3.2.1 Soil Infiltration Test
An infiltration test measures how much water infiltrates into the ground in a specific period of time. For accurate results the tests and measurements should be done at the same depth as the base of the planned pit or trench. Method
1. Force an open steel or plastic cylinder or tube (approximately 30 cm diameter) into the ground.
2. Insert a ruler or other measure marked in millimetres into the tube.
3. Fill the tube with clean water and measure the fall in water level over time. For example measurements can be taken at 5, 10, 20, 30 and 60 minutes.
4. Determine the infiltration rate for each time period in mm/day using the calculation below:
)day(min/ 1440(min) Time
(mm) level waterin Fall /day)L/m or(mm/day rate onInfiltrati 2
NOTE: mm/day and L/m2/day are the same unit, just expressed differently. Infiltration rate tables often use L/m2/day. 5. Calculate the average using the calculation below:
rates oninfiltrati of Number
rates oninfiltrati of Sum (mm/day) rate onInfiltrati Average
6. Estimate the infiltration rate for wastewater. To do this, use table 3.1.3.2 - Typical Infiltration Rates Comparing Clean Water and Wastewater (found below), and find the range that your rate fits in under the „clean water‟ column. From this value you can see the corresponding wastewater infiltration rate for that soil type.
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Table 3.1.3.2 - Typical Infiltration Rates Comparing Clean Water and Wastewater
Soil Type Description Infiltration Rate L/m2/day
Clean Water Wastewater
Gravel, coarse and medium sand
Moist soil will not stick together
1500-2400 50
Fine and loamy sand
Moist soil sticks together but will not form a ball
720-1500 33
Sandy loam and loam
Moist soil forms a ball but still feels gritty when rubbed between the fingers
480-720 24
Loam, porous silt loam
Moist soil forms a ball which easily deforms and feels smooth between the fingers
240-480 18
Silty clay loam and clay loam
Moist soil forms a strong ball which smears when rubbed but does not go shiny
120-240 8
Clay
Moist soil moulds like plasticine and feels sticky when wetter
24-120 Unsuitable for soak pits or trenches
(Harvey, Baghri, & Reed, 2002)
The infiltration rates for wastewater given in the table above are much lower than those for clean water. This is because the spaces between the soil particles become clogged by suspended particles and organic matter in the wastewater. Also, these rates are very likely to decrease over time.
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Infiltration Test Example:
Time from start (minutes) Fall in water level (mm) Infiltration rate (mm/day or L/m2/day)
5 4 1152
10 8 1152
20 11 792
30 14 672
60 16 384
Total 4152
Average 830.4
Example Calculations: At 5 minutes
)day/l/m or day/mm( 1152iR
)day(min/1440min)/mm(8.0iR
)day(min/1440min 5
4mm Rate onInfiltrati
2
At 10 minutes
)day/l/m or day/mm( 1152iR
)day(min/1440min)/mm(8.0iR
)day(min/1440min10
mm8iR
2
At 20 minutes
)day/l/m or(mm/day 792iR
)day(min/1440min)/mm(55.0iR
)day(min/1440min20
mm11iR
2
/day)L/m or(mm/day 8305
38467279211521152 rate onInfiltrati Average 2
Using table 3.1.3.2, the average rate calculated of 830 L/m2/day corresponds to the value for “fine, loamy sand” giving a wastewater infiltration rate of 33 L/m2/day.
Soil Type Description Infiltration Rate L/m2/day
Clean Water Wastewater
Fine and loamy sand
Moist soil sticks together but will not form a ball
720-1500 33
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3.3 Summary of Soak Pit and Infiltration Trench Equations
Use the information in this section as a reference to follow along with the examples in Section 3.2 and to work through the practice questions in Section 3.3.
Table 3.1.4.1 - Table of Equations
Dimension Formula Variables
Geometric Infiltration Area: Rectangular Soak Pit
)WL(D2iA
iA: Infiltration area (m2) D: Depth (m) L: Length (m) W: Width (m)
Geometric Infiltration Area: Circular Soak Pit
D14.3diA
iA: Infiltration area (m2) d: Diameter (m) D: Depth (m)
Geometric Infiltration Area: Infiltration Trench
DL2iA
iA: Infiltration area (m2) D: Depth (m) L: Length (m)
Usage Infiltration Area iR
QiA
iA: Infiltration area (m2) iR: Infiltration rate (l/m2/day) Q: Wastewater loading (L/day)
Infiltration Trench Length ADV D: Depth (m) A: Area (m2)
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Table 3.1.4.2 - Typical Infiltration Rates According to Soil Type
Soil Type Physical Description Infiltration Rate of Wastewater(L/m2/day)
Gravel, coarse and medium sand
Moist soil will not stick together
50
Fine and loamy sand Moist soil sticks together but will not form a ball
33
Sandy loam and loam Moist soil forms a ball but still feels gritty when rubbed between the fingers
24
Loam, porous silt loam Moist soil forms a ball which easily deforms and feels smooth between the fingers
18
Silty clay loam and clay loam Moist soil forms a strong ball which smears when rubbed but does not go shiny
8
Clay* Moist soil moulds like plasticine and feels sticky when wetter
Unsuitable for soak pits or infiltration trenches.
Depth (D)
Diameter (d)
Circular Pit
Length (L)
Depth (D)
Infiltration Trench
Length (L)
Depth (D)
Width (W)
Rectangular Pit
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We are using an infiltration rate of 24 (L/m2/day) because we are digging in sandy loam.
We are trying to find the depth (D) of the pit.
3.4 Example Questions
3.4.1 Rectangular Soak Pit Calculation – Finding Depth
A family needs to dispose of 100 litres of wastewater per day
They want the soak pit to have a length of 1.2 metres and a width of 1.0 metre
They are digging in sandy loam How deep should their soak pit be?
Solution Step 1: Known information – Write down the variables and their values. Identify the variable that you need to solve for.
? Depth
/day)metres(litres/ 24 Rate onInfiltrati
metre 1.0 Width
metres 1.2 Length
y)(litres/da 100 Loading Wastewater
rRectangula Shape
2
D
iR
W
L
Q
Step 2: Draw and Label Your Diagram – Draw a diagram of the pit and label all dimensions.
Length (L)
1.2 m
Depth (D) ?
Width (W)
1.0 m
Rectangular Pit
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We are finding the value for iA (infiltration area) first because we know the values for both Q (wastewater loading) and iR (soil infiltration rate).
Step 3: Formulas - Write down the formula for the variable you are trying to solve for. Check if you have the value for each variable in it. If values are not given, find an equation to give you the missing value of the variable you want. Be sure that you are using the formula for the right shape.
)WL(2
iAD
m0.1W
m2.1L
?iA
iR
QiA
)day/m/L(24iR
)day/L(100Q
2
Step 4: Fill in the formula that you know the value of all the variables for.
2
2
m2.4iA
)day/m/L(24
)day/L(100iA
iR
QiA
The first equation gives the depth but we don’t know the value of iA (infiltration area).
The second equation gives the value for iA (infiltration area).
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From the previous equation we now know the value of iA. We can now solve for D.
Fill in all the values for the variables.
Do the addition inside the brackets first.
Do the multiplication.
Do the division.
Step 5: Fill in the formula that you know the value of all the variables for.
m0.1D
m4.4
m2.4D
m2.22
m2.4D
)m0.1m2.1(2
m2.4D
)WL(2
iAD
2
2
2
Step 6: Write out the answer. The depth must be 1.0 metre for the pit to infiltrate 100 litres of wastewater each day. This is assuming the pit has a slab for a cover. If soil will be used for cover at least 0.2 metres must be added to the depth.
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We are using an infiltration rate of 18 (L/m2/day) because we are digging in porous silt loam.
We are trying to find the depth (D) of the pit.
3.4.3 Circular Soak Pit Calculation – Finding Depth
A family needs to dispose of 100 litres of wastewater per day
They want the soak pit to have a diameter of 1.3 metres
They are digging in porous silt loam How deep should their soak pit be?
Solution Step 1: Known information – Write down the variables and their values. Identify
the variable that you need to solve for.
? Depth
)day/tres(litres/me 18 Rate onInfiltrati
metres 1.3 Diameter
y)(litres/da 100 Loading Wastewater
circular Shape
2
D
iR
d
Q
Step 2: Draw and Label Your Diagram – Draw a diagram of the pit and label all
dimensions.
Depth (D) ?
Diameter (d) 1.3 m
Circular Pit
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We are finding the value for iA (infiltration area) first because we know the values for both Q (wastewater loading) and iR (soil infiltration rate).
Step 3: Formulas - Write down the formula for the variable you are trying to solve for. Check if you have the value for each variable in it. If values are not given, find an equation to give you the missing value of the variable you want. Be sure that you are using the formula for the right shape.
d14.3
iAD
m3.1d
?iA
iR
QiA
)day/m/L( 18iR
)day/L( 100Q
2
Step 4: Fill in the formula that you know the value of all the variables for.
2
2
m6.5iA
)day/m/L(18
)day/L(100iA
iR
QiA
The first equation gives the depth but we don’t know the value of iA (infiltration area).
The second equation gives the value for iA (infiltration area).
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From the previous equation we now know the value of iA. We can now solve for D.
Fill in all the values for the variables.
Do the multiplication first.
Do the division.
Step 5: Fill in the formula that you know the value of all the variables for.
m4.1D
m1.4
m6.5D
m3.114.3
m6.5D
d14.3
iAD
2
2
Step 6: Write out the answer. The depth must be 1.4 metres for the pit to infiltrate 100 litres of wastewater each day. This is assuming the pit has a slab for a cover. If soil will be used for cover at least 0.2 metres must be added to the depth.
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We are using an infiltration rate of 24 (L/m2/day) because we are digging in sandy loam.
We are trying to find the length (L) of the trench.
3.4.4 Infiltration Trench – Finding Length
A family needs to dispose of 80 litres of wastewater per day
They want the walls of their infiltration trench to be 0.5 metres deep
They are digging in sandy loam How long should their trench pit be?
Solution Step 1: Known information – Write down the variables and their values. Identify the variable that you need to solve for.
? Lenght
metres 0.5 Depth
/day)metres(litres/ 24 Rate onInfiltrati
y)(litres/da 80 dInfiltrate be to r Wastewateof Amount
2
L
D
iR
Q
Step 2: Draw and Label Your Diagram – Draw a diagram of the pit and label all dimensions.
Length (L)
?
Depth (D)
0.5 m
Infiltration Trench
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We are finding the value for iA (infiltration area) first because we know the values for both Q (wastewater loading) and iR (soil infiltration rate).
Step 3: Formulas - Write down the formula for the variable you are trying to solve for. Check if you have the value for each variable in it. If values are not given, find an equation to give you the missing value of the variable you want. Be sure that you are using the formula for the right shape.
D2
iAL
m5.0D
?iA
iR
QiA
)day/m/L(24iR
)day/L(80Q
2
Step 4: Fill in the formula that you know the value of all the variables for.
2
2
m33.3iA
)day/m/L(24
)day/L(80iA
iR
QiA
The first equation gives the length but we don’t know the value of iA (infiltration area).
The second equation gives the value for iA (infiltration area).
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From the previous equation we now know the value of iA. We can now solve for L.
Fill in all the values for the variables.
Do the multiplication.
Do the division.
Step 5: Fill in the formula that you know the value of all the variables for.
m33.3L
m0.1
m33.3L
m5.02
m33.3L
D2
iAL
2
2
Step 6: Write out the answer. The length must be 3.33 metres for the pit to infiltrate 80 litres of wastewater each day. A soil cover at least 0.2 metres must be added to the depth.
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3.5 Practice Questions
3.5.1 Rectangular Soak Pit - Finding Depth
Question 5
A family wants to build a rectangular soak pit
They need to dispose of 120 litres of wastewater each day
They want to make it 1.2 x 1.2 metres
They are digging in a soil that sticks together but won‟t form a ball
How deep should their pit be?
Calculations
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We are using an infiltration rate of 33(L/m2/day) because the description indicates that we are in fine and loamy sand.
We are trying to find the depth (D) of the rectangular pit.
Solution Step 1: Known information – Write down the variables and their values. Identify the variable that you need to solve for.
Step 2: Draw and Label Your Diagram – Draw a diagram of the pit and label all
dimensions.
? Depth
/day)metres(litres/ 33 Rate onInfiltrati
metre 1.2 Width
metres 1.2 Length
y)(litres/da 120 dInfiltrate be to r Wastewateof Amount
rRectangula Shape
2
D
iR
W
L
Q
Length (L)
1.2 m
Depth (D) ?
Width (W)
1.2 m
Rectangular Pit
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We are finding the value for iA (infiltration area) first because we know the values for both Q (wastewater loading) and iR (soil infiltration rate).
Step 3: Formulas - Write down the formula for the variable you are trying to solve for. Check if you have the value for each variable in it. If values are not given, find an equation to give you the missing value of the variable you want. Be sure that you are using the formula for the right shape.
)WL(2
iAD
m2.1W
m2.1L
?iA
iR
QiA
)day/m/L(33iR
)day/L(120Q
2
Step 4: Fill in the formula that you know the value of all the variables for.
2
2
m6.3iA
)day/m/L(33
)day/L(120iA
iR
QiA
The first equation gives the depth but we don’t know the value of iA (infiltration area).
The second equation gives the value for iA (infiltration area).
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From the previous equation we now know the value of iA. We can now solve for D.
Fill in all the values for the variables.
Do the addition inside the brackets first.
Do the multiplication.
Do the division.
Step 5: Fill in the formula that you know the value of all the variables for.
m8.0D
m8.4
m6.3D
m4.22
m6.3D
)m2.1m2.1(2
m6.3D
)WL(2
iAD
2
2
2
Step 6: Write out the answer. The depth must be 0.8 metres for the pit to infiltrate 120 litres of wastewater each day. This is assuming the pit has a slab for a cover. If soil will be used for cover at least 0.2 metres must be added to the depth.
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3.5.3 Circular Soak Pit – Finding Depth
A family needs to get rid of 140 litres of wastewater per day
They want the soak pit to have a diameter of 1.2 metres
They are digging in a sandy loam
How deep should their soak pit be?
Calculations
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We are using an infiltration rate of 24 (L/m2/day) because we are digging in sandy loam.
We are trying to find the depth (D) of the pit.
Solution Step 1: Known information – Write down the variables and their values. Identify
the variable that you need to solve for.
Step 2: Draw and Label Your Diagram – Draw a diagram of the pit and label all
dimensions.
? Depth
)day/tres(litres/me 24 Rate onInfiltrati
metres 1.2 Diameter
y)(litres/da 140 dInfiltrate be to r Wastewateof Amount
circular Shape
2
D
iR
d
Q
Depth (D)
?
Diameter (d)
1.2 m
Circular Pit
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We are finding the value for iA (infiltration area) first because we know the values for both Q (wastewater loading) and iR (soil infiltration rate).
Step 3: Formulas - Write down the formula for the variable you are trying to solve for. Check if you have the value for each variable in it. If values are not given, find an equation to give you the missing value of the variable you want. Be sure that you are using the formula for the right shape.
d14.3
iAD
m2.1d
?iA
iR
QiA
)day/m/L( 24iR
)day/L( 140Q
2
Step 4: Fill in the formula that you know the value of all the variables for.
2
2
m8.5iA
)day/m/L(24
)day/L(140iA
iR
QiA
The first equation gives the depth but we don’t know the value of iA (infiltration area).
The second equation gives the value for iA infiltration area).
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From the previous equation we now know the value of iA. We can now solve for D.
Fill in all the values for the variables.
Do the multiplication first.
Do the division.
Step 5: Fill in the formula that you know the value of all the variables for.
m5.1D
m8.3
m8.5D
m2.114.3
m8.5D
d14.3
iAD
2
2
Step 6: Write out the answer. The depth must be 1.5 metres for the pit to infiltrate 140 litres of wastewater each day. This is assuming the pit has a slab for a cover. If soil will be used for cover at least 0.2 metres must be added to the depth.
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3.5.4 Infiltration Trench – Finding Length
A family wants to build an infiltration trench
They need to dispose of 80 litres of wastewater each day
The depth of the trench walls is 0.4 metres
They are digging in a soil that forms a ball which easily deforms and feels smooth between the fingers
How long should their trench be?
Calculations
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We are using an infiltration rate of 8 (L/m2/day) because the description indicates that we are digging in silty clay and clay loam.
We are trying to find the length (L) of the trench.
Solution Step 1: Known information – Write down the variables and their values. Identify the variable that you need to solve for.
? Lenght
metres 0.4 Depth
/day)metres(litres/ 8 Rate onInfiltrati
y)(litres/da 80 dInfiltrate be to r Wastewateof Amount
2
L
D
iR
Q
Step 2: Draw and Label Your Diagram – Draw a diagram of the pit and label all dimensions.
Length (L)
?
Depth (D)
0.4 m
Infiltration Trench
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We are finding the value for iA (infiltration area) first because we know the values for both Q (wastewater loading) and iR (soil infiltration rate).
Step 3: Formulas - Write down the formula for the variable you are trying to solve for. Check if you have the value for each variable in it. If values are not given, find an equation to give you the missing value of the variable you want. Be sure that you are using the formula for the right shape.
D2
iAL
m4.0D
?iA
iR
QiA
)day/m/L(8iR
)day/L(80Q
2
Step 4: Fill in the formula that you know the value of all the variables for.
2
2
m10iA
)day/m/L(8
)day/L(80iA
iR
QiA
The first equation gives the length but we don’t know the value of iA (infiltration area).
The second equation gives the value for iA (infiltration area).
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From the previous equation we now know the value of iA. We can now solve for L.
Fill in all the values for the variables.
Do the multiplication.
Do the division.
Step 5: Fill in the formula that you know the value of all the variables for.
m5.12L
m8.0
m10L
m4.02
m10L
D2
iAL
2
2
Step 6: Write out the answer. The length must be 12.5 metres for the pit to infiltrate 80 litres of wastewater each day. This can also be split into two trenches, each 6.3 metres long. A soil cover of at least 0.2 metres must be added to the depth.
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4 References
Harvey, P., Baghri, S., & Reed, B. (2002). Emergency Sanitation: Assessment and Programme Design. Loughborough, UK: WEDC.